The commercialization of high-critical temperature superconducting (HTS) devices for electric power applications is presently stalled by a hiatus in the advancement of the current-carrying capacity of long-length conductors. In the case of the silver-sheathed (Bi,Pb)2Sr2Ca2Cu3Oy (Ag/Bi-2223) composite conductor the critical current density appears to be limited by interruptions in the Bi-2223 grain colony microstructure. Whereas, uniform thin (sub-micron) films of Bi-2223 deposited on smooth substrates have been found to carry in excess of 1,000 kA/cm2 of superconductor at 77 K, the best Ag/Bi-2223 composites seldom exceed 70 kA/cm2 at 77 K. Examination of some of the better performing Ag/Bi-2223 composites shows that the Bi-2223 grain colony microstructure is disrupted in many places by large non-superconducting second phases (NSPs) that are created as side products of the Bi-2223 formation reaction. What is needed is a heat treatment protocol that either eliminates the NSPs or reduces whatever NSPs there are to the smallest possible size (preferably sub-micron).